A Single Logical Framework for Ontology, Mathematics, and Physics

When we derive a time-dependent equation, mathematically we represent time along its own axis, but doing so is not a derivation of what time is ontologically; it is an assumption that allows us to express reality in terms of the tool (mathematics). If we were to use a different tool, say logic or text, we might assume that time is something else (e.g., a property). Thus, just because a tool works in describing reality doesn't imply that the assumption needed to express reality in terms of the tool is ontologically accurate. Although the expressive nature of mathematics allows us to predict aspects like black holes and antiparticles, it tells us nothing about the ontological meaning of concepts such as time and space, and therefore it doesn't tell us anything about the universes actual geometry; equations merely establish mathematical relationships between variables. To derive the ontological structure that all other tools describe, notice that every tool that we have for understanding reality (philosophy, mathematics, logic, etc.) uses logic as a foundation, not mathematics (these are not the same). It follows that we must establish a method to derive ontology through the direct application of logic, the same way that mathematics is developed, such that our equations of physics describe its behavior.